Topologically multiplexed optical data communication

ABSTRACT

Systems and methods for encoding information in the topology of superpositions of helical modes of light, and retrieving information from each of the superposed modes individually or in parallel. These methods can be applied to beams of light that already carry information through other channels, such as amplitude modulation or wavelength dispersive multiplexing, enabling such beams to be multiplexed and subsequently demultiplexed. The systems and methods of the present invention increase the number of data channels carried by a factor of the number of superposed helical modes.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a Continuation of U.S. application Ser. No.12/477,584, filed Jun. 3, 2009, which is a continuation of Ser. No.11/222,469, filed Sep. 8, 2005, which claims priority from ProvisionalApplication U.S. Application 60/608,657, filed Sep. 10, 2004,incorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

Optical data communication typically involves modulating the amplitudeand wavelength of a beam of laser light, and detecting that modulationdownstream. The present invention is directed to a complementaryapproach to conveying information on a beam of light based on theproperties of helical optical modes.

A helical mode is characterized by the corkscrew-like topology of itswave fronts, which can be described by a real-valued phase function:φ({right arrow over (ρ)})=lθ,  (1)where {right arrow over (ρ)}=(ρ,θ) is the position in a plane transverseto the beam's axis, with θ being the polar angle, and l is an integralwinding number known as the topological charge that describes the pitchof the helix. This phase establishes the beam's topology through thegeneral expression for the magnitude of the electric field in acollimated beam,E _(l)({right arrow over (ρ)})=υ_(l)({right arrow over(ρ)})exp(iφ({right arrow over (ρ)}))exp(iφ _(l)),  (2)where υ_(l)({right arrow over (ρ)}) is the real-valued amplitude profileand φ_(l) is an arbitrary constant phase. A general superposition ofhelical modes can be written as

$\begin{matrix}{{E( \overset{arrow}{\rho} )} = {\sum\limits_{l = {- \infty}}^{\infty}\;{{E_{l}( \overset{arrow}{\rho} )}.}}} & (3)\end{matrix}$

If it is assumed that all the beams in the superposition have the sameamplitude profile, υ({right arrow over (ρ)}) perhaps with differentamplitudes, α_(l), then

$\begin{matrix}{{{{E( \overset{arrow}{\rho} )} = {\sum\limits_{l = {- \infty}}^{\infty}\;{\alpha_{l}{\upsilon( \overset{arrow}{\rho} )}{\exp( {{\mathbb{i}}\;{\varphi( \overset{arrow}{\rho} )}} )}{\exp( {\mathbb{i}\phi}_{l} )}}}},}\;} & (4)\end{matrix}$with normalization

${\sum\limits_{l = {- \infty}}^{\infty}\;{\alpha_{l}}^{2}} = 1.$For the practical applications, only a limited set of the α_(l) will benon-zero.

SUMMARY OF THE INVENTION

The present invention relates in part to methods for transformingconventional beams of light into helical modes and superpositions ofhelical modes. The present invention also involves detecting helicalmodes and methods for parallel data extraction from superpositions ofhelical modes. The ability to encode and decode information carried in abeam's topology leads naturally to methods for topological datacommunication. A slight elaboration on this theme yields methods formultiplexing and demultiplexing beams of light that also carryinformation through other channels, such as amplitude modulations.

These and other objects, advantages and features of the invention,together with the organization and manner of operation thereof, willbecome apparent from the following detailed description when taken inconjunction with the accompanying drawings, wherein like elements havelike numerals throughout the several drawings described below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot showing radial intensity profiles for superpositions ofhelical modes created from a conventional flat-top beam with acomputer-designated phase-only diffractive optical element;

FIG. 2( a) is a representation of a helical beam with topological chargel being converted to a conventional non-helical beam by a DOE encoding atopological charge of −l; and FIG. 2( b) is a representation of ahelical beam if the DOE does not exactly cancel the input beam'shelicity, wherein the resulting beam still has a dark focus and will notbe detected by the photodetector.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The wave fronts of a helical beam may all meet along the optical axis ata topological singularity known as an l-fold screw dislocation.Conventional beams, by contrast, have no such defect. Introducing such adefect therefore transforms a conventional beam into a helical beam.There are numerous ways to accomplish this transformation and one of themost straightforward methods of transforming a conventional beam into ahelical beam is to sculpt the phase of the conventional beam's wavefronts according to Equation (1) discussed previously. This can beaccomplished by passing the beam of light through a piece of transparentmaterial with a helical surface relief, with the resulting local phaseshift being proportional to the local thickness of the material.

Another method for accomplishing this task is to employ a phase-onlyspatial light modulator (SLM), which is designed to shift the phase ofincident light by a programmable amount at each pixel in atwo-dimensional array. SLMs typically are designed to provide a range of2π radians of phase shift. Because a phase shift of 2π is equivalent toa zero phase shift, the helical profile, which covers an arbitrarilylarge range, can be mapped onto the device's dynamic range with themodulo operator: φ({right arrow over (ρ)}) mod 2π. Light operated on byan SLM picks up the phase factor, exp(iφ({right arrow over (ρ)}) thatdistinguishes the helical beam in Equation (2) from a conventional beam.

The phase pattern that implements this mode conversion is an example ofa phase-only hologram. Whereas an SLM allows for dynamicallyreconfigured holograms, some data communications applications also cantake advantage of various optical elements such as microfabricateddiffractive optical elements (DOEs) with fixed phase transfer properties(see FIGS. 2A and 2B).

The helical phase function, represented in Equation (1), creates ahelical beam 40 (see FIG. 2A) coaxial with an incident conventional beam15 (see FIG. 2A). This mode conversion may not occur with perfectefficiency. The result may therefore include an undiffracted portion ofthe original non-helical beam 15. To avoid this result, it may bedesirable to deflect the diffracted helical beam 40. This can beaccomplished by adding a phase function encoding a deflection by a wavevector {right arrow over (k)},φk({right arrow over (ρ)})={right arrow over (k)}·{right arrow over(ρ)}  (5)to the phase function encoding the mode conversion. The result is adeflected helical beam, with the undiffracted portion propagating in theundeflected direction.

FIG. 1 is a plot showing intensity profiles for superpositions ofhelical modes created from a conventional flattop beam 15 with acomputer-designed phase-only DOE 20 (see FIGS. 2A and 2B. The bold curveis computed for a superposition of eight helical modes with topologicalcharges l=11, 21, 31, 41, 51, 61, 71, and 81. The thin curve is for asuperposition with the components at l=21 and 71 excluded. Rescaling theazimuthal averages by the radial coordinate, r, makes clear that thesuperposed modes have equal power.

Superpositions of helical modes are created generally as follows. In ageneral superposition,

$\begin{matrix}{{E( \overset{arrow}{\rho} )} = {\sum\limits_{l = {- \infty}}^{\infty}\;{\alpha_{l}{\upsilon( \overset{arrow}{\rho} )}{\exp( {{\mathbb{i}}\lbrack {{l\;\theta} + {{\overset{arrow}{k}}_{l} \cdot \overset{arrow}{\rho}} + \phi_{l}} \rbrack} )}}}} & (6)\end{matrix}$

Created from a collimated beam with amplitude cross-section υ({rightarrow over (ρ)}). Even though the individual modes differ from the input15 beam by a pure phase factor, the sum also features amplitudemodulations. These amplitude modulations can be minimized, but might notbe altogether eliminated, by appropriately selecting the relativephases, φ_(l). Iterative and direct search algorithms are also availablefor computing phase-only holograms that can maximize diffraction intosuch superposed modes.

The data plotted with a bold curve in FIG. 1 were computed for asuperposition of eight modes ranging from l=11 to 81, created from asingle flat-top beam of light 15 with a phase-only hologram. This plotshows the beam's intensity averaged over angles, scaled by thecircumference. Removing two modes from the superposition results in aclearly measurable change in the intensities associated with thosemodes, and a far less substantial change in other neighboring modes'intensities.

Using these methods, a single conventional laser beam 15 or from otherlight sources 10 can be transformed into a superposition of helicalmodes, each traveling in an independently specified direction. Possibleexample configurations include multiple modes propagating in the samedirection, or the beams 40 with the same topological charge traveling indifferent directions.

A helical mode's topology endows it with an important property for datacommunications. Because all angles are present along the beam's axis,all phases are present. Typically, the resulting destructiveinterference causes the beam 40 to be dark along its axis, regardless ofthe amplitude profile υ({right arrow over (ρ)}). The beam's intensity isredistributed into a ring of light of radius R_(l). The radius of thedark core increases with the beam's topological charge l. In the specialcase that the amplitude profile is that of a Laguerre-Gaussian eigenmodeof the Helmholtz equation, R_(l), is proportional to √{square root over(l)}. This is a conventional concept in the art (see, for example, M. J.Padgett and L. Allen. “The Poynting vector in Laguerre-Gaussian modes.”Optics Communications 121, 36-40 (1995)). More generally, for Gaussianbeams, flat-top beams, and other common profiles, it is conventionalthat R_(l) is proportional to l, (see, for example, J. E. Curtis and D.G. Grier. “Structure of optical vortices.” Physical Review Letters 90,133901(2003)).

A photodetector 200 whose active area has dimensions substantiallysmaller than R_(l) for a given value of will register no light whendirectly illuminated by a helical beam 40. After operation by thedetecting hologram it is then a conventional beam and the beam would nowactivate the photodetector. FIG. 2( a) is a representation showing howthe helical beam 40 with topological charge l is converted to aconventional non-helical beam 50 by a DOE 60 encoding a topologicalcharge of −l. The resulting l=0 mode can be focused onto thephotodetector 200 and measured. FIG. 2( b) shows how, if the DOE 60 doesnot exactly cancel the input beam's helicity, the resulting beam 50still has a dark focus and will not be detected by the photodetector200.

Recalling that diffractive optical elements are capable of changing abeam's topological charge suggests the method for specifically detectinglight in a particular topological mode depicted in FIGS. 2( a) and (b).The beam of light 15 is operated on by a diffractive optical element 20encoding a helical mode with topological charge −l. Any component of thebeam 40 carrying topological charge l is thereby converted to thenon-helical beam 50. After operation by the detecting hologram it isthen a conventional beam and the beam can be focused to a bright spot.Other modes with l′≠l will be transformed to helical anodes withtopological charge l′−l≠0 and will remain dark on axis using lens 55.Distinguishing different modes can be facilitated by focusing theDOE-transformed beam 50 onto an aperture 80 that will block stray lightfrom undesired modes, thereby improving the detector's selectivity.

Detecting helical modes does not suffer from limited diffractionefficiency to the same extent that creating them does. In particular, ifsome part of the selected helical mode is not operated on by thedetecting DOE 100, then that part will not be detected. Other modes willnot be spuriously detected, however, so that faithful mode detection canproceed with an imperfect DOE.

The same selectivity is obtained if the detection DOE 100 also deflectsthe beam 50. In this case, the detector is centered on the deflectedbeam's wave vector {right arrow over (k)}_(l) rather than the originalbeam's optical axis. The detector's DOE can select and deflect differentmodes into different directions, each of which can be outfitted with aphotodetector. This permits parallel detection of data encoded insuperpositions of helical beams. For example, the eight modes projectedin FIG. 1 can each be read out separately by such a spatially resolvedparallel topological detector. In practice, each of the superposed modesis deflected into all of the possible output directions. Only theselected mode for a particular direction focuses on the associateddetector, however.

The simplest form of topological data communication is to modulate thetopological charge of a beam of light with a time-varying helicaldiffractive optical element and reading out the result with detectorssuch as those described in the previous section. Data can be encoded inthe time-dependent sequence of topological charges in the beam, with thesimplest modulation involving switching between a state with l=0 andanother with l≠0. A more sophisticated approach encodes data in asequence of several values of l, each of which can be read out with aseparate topological charge detector. In a still more sophisticatedapproach, data can be encoded in multiple simultaneous topologicalchannels using a superposition of helical states such as that in FIG. 1.

The detector used to read out the topological charge also may betime-dependent, opening up the ability to hop among topological datachannels. This may be useful in applications akin to frequency hoppingin secure radio communications.

Beams of light that already carry data through other channels, such asamplitude modulation, wavelength modulation or phase modulation, alsocan be transformed into helical beams and superposed with other helicalbeams. Each data stream then is capable of traveling through aparticular topological channel in parallel with others.

In one implementation, a plurality of information carrying beams allilluminate an appropriately designed diffractive optical element, eachat a particular angle. The diffractive optical element deflects all ofthe beams into one or more selected directions, endowing each beam witha specific topological charge. The result is one or more beams carryinga superposition of different helical modes, each carrying informationencoded in other characteristics of the beam. This type of beam isreferred to as a topologically multiplexed beam.

The multiplexed beam can be demultiplexed with a similar DOE thatdissects the superposed beam into the individual constituents, one pertopological channel. These reconstituted beams can be further analyzedwith other techniques. The simplest implementation of this idea woulduse two copies of the same DOE, one to multiplex the beams, and anotherturned backward to demultiplex it.

The system and method of the present invention can be incorporated intoa number of different applications. For example, a beam that alreadycarries multiple data channels can be taken to undergo wavelengthdivision multiplexing, where multiple wavelengths of light can be passedover a single fiber, to impress upon it a helical phase profile, therebymaking the beam amenable to topological multiplexing. Such a systemwould allow for a significantly increased number of topologicalchannels, resulting in a multiplication of the bandwidth of a particularcommunication channel.

Additionally, the present invention could also be used to create anencryption system. This encryption system may further be high high-speedand/or an all-optical encryption system. Furthermore, the superpositionof topological states itself can be used to convey information. Onecould also therefore encode information in the time-dependentsuperposition of topological modes, in addition to any other informationcarried within the input beams themselves. This can be used, forexample, to maintain an encoded checksum for the data carried on themultiple data channels to authenticate the sender of information. Thisprocess can constitute an additional, potentially secure, data channelin its own right. The present invention may provide for securityadvantages and advances in secure communication which deter or preventintrusion, eavesdropping, or unauthorized access, reception or decodingof transmitted information. The present invention may be used at leastin part for quantum communications, quantum cryptography, encoding ofclassical or quantum information, and in conjunction with varioustransmission media including free space communications.

In other embodiments of the invention various higher-order Gaussianbeams can be used as well as Laguerre-Gaussian (LG) modes, higher ordermodes, and/or orbital angular momentum.

In yet another embodiment the present invention may also employ variousoptical elements which include but are not limited to diffractiveoptical elements (DOEs) and which may further include microfabricateddiffractive DOEs with fixed phase transfer properties.

Further embodiments may include multiple transmitters and/or detectors,adaptive optics for such purposes as correction of degradation intransmission medium (e.g. fiber, air, etc) and may adjust for angularmisalignment or lateral misalignment (e.g. of transmitter and/orreceiver or detector).

While several embodiments have been shown and described herein, itshould be understood that changes and modifications can be made to theinvention without departing from the invention in its broader aspects.Various features of the invention are defined in the following Claims:

1. A method of generating a topologically multiplexed light beam for usein optical data communications, comprising the steps of: providing atleast one information-carrying light beam illuminating a first opticalelement; using the first optical element to deflect the at least oneinformation-carrying light beam into at least one selected direction;providing the at least one information-carrying light beam with aplurality of specific topological charges imposed on the light beam,thereby providing a resultant multiplexed light beam suitable for use inoptical data communications via different topological channels; andusing a second optical element to divide the at least one resultant beaminto a plurality of constituent beams, wherein the first and secondoptical elements comprise at least two optical elements, with the secondoptical element being oriented backwards relative to the first opticalelement on an optical axis.
 2. The method as defined in claim 1 whereinthe multiplexed light beam includes a superposition of different helicalmodes.
 3. The method of claim 1 wherein deflection of theinformation-carrying light beam comprises adding a phase functionφ_(k)({right arrow over (ρ)})={right arrow over (k)}·{right arrow over(ρ)}, to the light beam.
 4. The method of claim 1 further including thestep of processing at least one of the information-carrying beam and theresultant light beam by at least one of wavelength modulation, amplitudemodulation, phase modulation, and time pulse modulation.
 5. The methodof claim 1 further including the step of generating a plurality of datachannels from the resultant light beam.
 6. A method of providingtopological data communication, comprising the steps of: a source oflight for providing a beam of light for carrying information wherein thefirst diffractive optical element introduces a superposition of theplurality of topological charges; using a first diffractive opticalelement to provide a multiplexed light beam having an imposed pluralityof topological charges wherein data from the multiplexed light beam isencoded in the sequence of topological charges, creating a plurality oftopological data channels for use in data communication; providing asecond diffractive optical element to change the multiplexed light beaminto a de-multiplexed light beam; and reading out the multiplexed lightbeam using a detector to provide information for data communication. 7.The method of claim 6 wherein the sequence of topological charges istime dependent and the time-dependent sequence of topological chargesmodulates between at least a first state and a second state.
 8. Themethod of claim 6 further comprising the step of moving among theplurality of topological data channels using the time dependentdetector.
 9. The method of claim 6 further including the step selectedfrom the group consisting of at least one of processing the beam oflight, processing the multiplexed light beam, performing a wavelengthmodulation, performing an amplitude modulation, performing a phasemodulation and performing a time pulse modulation each for use in datacommunication.
 10. The method of claim 6 wherein data from themultiplexed light beam is encoded in multiple simultaneous topologicalchannels using a superposition of helical states.
 11. The method ofclaim 6 wherein the detector operates in at least one of a timedependent manner and in a manner to detect an individual topologicalchannel of a plurality of topological channels disposed in parallel. 12.The method of claim 6 wherein the detector comprises a diffractiveoptical element.
 13. The method of claim 6 wherein the detectorcomprises a spatially resolved parallel topological detector.
 14. Themethod of claim 6 further including the step of processing at least oneof the information-carrying beam of light and the multiplexed light beamby at least one of wavelength modulation, amplitude modulation, phasemodulation, and time pulse modulation.
 15. The method of claim 6 furtherincluding the step of generating a plurality of data channels from theresultant light beam.
 16. A system for processing a topologicallymultiplexed light beam for use in optical data communications,comprising at least one of the components, a first diffractive opticalelement for acting on an input light beam having a phase, the firstdiffractive optical element constructed to provide a selected pluralityof topological charges to create an output light beam of at least onemultiplexed resultant light beam carrying a superposition of differenthelical modes on the multiplexed resultant light beam to enable datacommunication; and a second diffractive optical element for deflectingthe multiplexed resultant light beam away from an undiffracted portionof the input light beam and a detector for sensing the diffractedmultiplexed light communication beam, thereby enabling use of themultiplexed light beam for optical data communications.
 17. The systemof claim 16 wherein the first diffractive optical element processes theresultant light beam by at least one of wavelength modulation, amplitudemodulation, phase modulation, and time pulse modulation.
 18. The systemof claim 16 further including a component for generating a plurality ofdata channels from the resultant light beam.
 19. A method of analyzingtopological data communication, comprising the steps of: using a firstdiffractive optical element to operate on a beam of light alreadycarrying modulated information selected from the group of amplitude,wavelength and phase, and including a multiplexed light beam; andoperating on the multiplexed light beam having an imposed plurality oftopological charges to read out the multiplexed light beam using adetector to provide data communication information wherein the detectoroperates in at least one of a time dependent manner and in a manner todetect an individual topological channel of a plurality of topologicalchannels disposed in parallel.
 20. The method of claim 19 furthercomprising the step of moving among the multiplexal light beam havingthe plurality of topological charges using the time dependent detector.21. The method of claim 19 further including the step selected from thegroup consisting of at least one of processing the beam of light,processing the multiplexed light beam, performing a wavelengthmodulation, performing an amplitude modulation, performing a phasemodulation and performing a time pulse modulation each for use inprocessing the data communication information.
 22. The method of claim19 wherein data from the multiplexed light beam is encoded in multiplesimultaneous topological channels using a superposition of helicalstates present in the first diffractive optical element.
 23. The methodof claim 19 wherein the detector comprises a diffractive opticalelement.
 24. The method of claim 19 wherein the detector comprises aspatially resolved parallel topological detector.
 25. The method ofclaim 19 further including the step of generating a plurality of datachannels from the multiplexed light beam having been read out.
 26. Amethod of providing topological data communication, comprising the stepsof: providing a beam of light for carrying information; providing amultiplexed light beam having an imposed plurality of topologicalcharges; and reading out the multiplexed light beam using a detector toprovide information for data communication, operation of the detectorbeing in at least one of a time dependent manner and in a manner todetect an individual topological channel of a plurality of topologicalchannels disposed in parallel.